Calculating the Distance for the Death Star to Appear as Large as the Moon in Earth's Sky

Welcome to this article where we explore the fascinating world of celestial objects and their apparent sizes from our vantage point on Earth. The iconic Death Star from the Star Wars universe has always been a source of fascination, leading us to ask: at what distance would the Death Star appear to have the same apparent size as our Moon?

Understanding Apparent Size and Angle

The apparent size of an object in the sky is determined by its angular diameter, which is the angle subtended by the object at the observer's eye. The Moon, for instance, has an angular diameter of about 30 arc-minutes, which is approximately 0.5 degrees.

Death Star Dimensions

The original Death Star in the Star Wars universe, as per canon, has a diameter of 120 kilometers. This information is crucial to our calculations.

Calculating the Required Distance

To calculate the distance from the Earth at which the Death Star would appear as large as the Moon, we use the formula:

distance size / 2 * sin(angle/2)

Step-by-Step Calculation

Let's break this down into steps:

Capture the Necessary Data: We know the diameter of the Death Star (120 km) and the angular diameter of the Moon (30 arc-minutes or 0.5 degrees). Convert Degrees to Radians: For precise calculation, convert the angle from degrees to radians because trigonometric functions in most mathematical contexts use radians. Apply the Formula: Substitute the values into the formula to find the distance.

Performing the Calculation

First, we need to convert the Moon's angular diameter from arc-minutes to radians:

0.5 degrees * (π / 180) radians/degree 0.0087266 radians

Now, replacing the values into the formula:

distance 120 km / (2 * sin(0.0087266 / 2))

Solving the above, we find:

sine(0.0043633) ≈ 0.0043633 (using small angle approximation sin(x) ≈ x for very small x)

distance 120 km / (2 * 0.0043633) ≈ 13,683.7 km

This means the Death Star needs to be approximately 13,683.7 km above the Earth's surface to appear as large as the Moon.

Comparing with Earth's Orbits

This distance is closer to, but not at, a geosynchronous orbit. A geosynchronous orbit is about 35,786 km above the Earth's surface, which means the Death Star would be in a much lower orbit than a geosynchronous satellite.

Conclusion

Thus, from an Earth-like planet, the Death Star would need to orbit around 13,683.7 km above the surface to appear as large as the Moon. This not only highlights the vast scale of the Death Star but also provides a window into the complex and fascinating field of astronomical measurements and calculations.

Further Reading

Apollo 16 Mission How Did the Moon Appear to Apollo 11 Astronauts?

Keywords

Death Star, Moon, astronomical distance, apparent size, orbit calculation